Question

Benzoic acid when shaken with mixtures of benzene and water undergoes dimerisation in benzene. The distribution law applicable here is (a) \(\frac{C_{1}}{C_{2}}=K_{D}\) (b) \(\frac{C_{1}}{\sqrt[3]{C_{2}}}=K_{D}\) (c) \(\frac{C_{1}}{\sqrt[2]{C_{2}}}=K_{D}\) (d) none of these

Short answer

The correct distribution law for the dimerisation of benzoic acid in a mixture of benzene and water is \(\frac{C_{1}}{\sqrt[2]{C_{2}}}=K_{D}\), which fall under option (c).

Step-by-step solution

Understand the problem

The original distribution law is \(K_{D}=\frac{C_{1}}{C_{2}}\), where \(C_{1}\) and \(C_{2}\) are equilibrium concentrations in two phases. But here, benzoic acid undergoes dimerisation, where two molecules combine to form a dimer. Our task is to determine how this dimerisation process affects the distribution law.

Analyze the effect of dimerisation on the distribution law

Dimerisation means two molecules of benzoic acid combine to form a dimer. Hence, the concentration of benzoic acid in the benzene phase will be halved. Since only one molecule of benzoic acid is moving to the benzene phase instead of two, this will affect the distribution law since the amount transferred is reduced.

Formulate the distribution law for benzoic acid

Taking into account the dimerisation, the distribution law will become \(K_{D}=\frac{C_{1}}{\sqrt[2]{C_{2}}}\) because the concentration of benzoic acid in benzene phase is halved due to dimerisation. Thus, to equate the law, the concentration in the water phase should be square rooted.

Key concepts

Dimerisation

Dimerisation is an interesting process in which two identical molecules bind together to form a single unit called a dimer. This effect is crucial when studying chemical reactions and various equilibria in chemistry. In particular, when benzoic acid, a common carboxylic acid, is placed in benzene, it undergoes dimerisation. This occurs because benzoic acid molecules have a tendency to form hydrogen bonds with each other, leading two molecules to pair up. When dimerisation happens in the context of a distribution law problem, it changes how we calculate concentrations in different phases:

• The original concentration in the solution is reduced because one dimer is formed from two separate molecules.
• This affects equilibrium calculations as one must account for how many molecules are present as dimers.

Understanding dimerisation helps predict how different substances distribute themselves between different solvents and influences reaction dynamics.

Benzoic Acid

Benzoic acid is an aromatic carboxylic acid widely used in various chemical reactions and compositions. It is known for its capability to undergo reactions such as esterification, and notably, in this context, dimerisation. In the benzoic acid structure, the carboxyl group ( -COOH) significantly impacts its chemical behavior. When benzoic acid is mixed with benzene, its likelihood of forming dimers is due to the hydrogen bonding properties inherent in its structure. This dimerisation is crucial in understanding chemical equilibria, as it can shift the balance of reactants and products, inevitably affecting how benzoic acid will distribute between benzene and water phases. Grasping the attributes of benzoic acid helps predict these changes and underscores its importance in various chemical and industrial processes.

Phase Equilibrium

Phase equilibrium occurs when the concentrations of chemical species do not change with time. This dynamic balance exists because the rate of transfer between two phases is equal. In our context, we're looking at two phases specifically: benzene and water, where benzoic acid is distributed. When benzoic acid undergoes dimerisation in benzene, it impacts the phase equilibrium. The concentration of benzoic acid in each phase reaches a point where movement between them happens at equal rates, even if it seems static. Key points about phase equilibrium include:

• The equilibrium constants specific to each phase remain constant over time.
• It supports the theoretical prediction of how substances behave when multiple phases are present.

This concept is important because it helps predict how benzoic acid's distribution and dimerisation affect its availability in each solvent.

Equilibrium Concentrations

Equilibrium concentrations describe the steady-state levels of substances within a system at equilibrium. In a distribution scenario, like benzoic acid and its phases, it's crucial to determine these concentrations accurately. In the given situation, the concentration of benzoic acid is modified by its ability to form dimers in the benzene, affecting phase comparison, and thus the distribution law. This effect means that the movement of benzoic acid between benzene and water phases reaches a balance that is influenced by dimerisation. To assess the equilibrium concentration properly:

• One must consider all molecules, including dimers, when calculating concentrations.
• Equilibrium is attained when the amount entering one phase is equal to that leaving, maintaining constants described by laws like the distribution law, adjusted for factors like dimerisation.

Having a clear understanding of equilibrium concentrations ensures that chemical distributions are interpreted correctly, especially in multi-phase systems.